Question: Simplify the following expression: $t = \dfrac{-10a^3 - 10a^2}{26a^2}$ You can assume $a \neq 0$.
Explanation: Find the greatest common factor of the numerator and denominator. The numerator can be factored: $-10a^3 - 10a^2 = - (2\cdot5 \cdot a \cdot a \cdot a) - (2\cdot5 \cdot a \cdot a)$ The denominator can be factored: $26a^2 = (2\cdot13 \cdot a \cdot a)$ The greatest common factor of all the terms is $2a^2$ Factoring out $2a^2$ gives us: $t = \dfrac{(2a^2)(-5a - 5)}{(2a^2)(13)}$ Dividing both the numerator and denominator by $2a^2$ gives: $t = \dfrac{-5a - 5}{13}$